By "thinking rationally", you must mean epistemically, not instrumentally.
If (to use as Less-Wrong-politically-neutral an allegory as I can) you are vastly outnumbered by citizens who are wondering if maybe those birds were an omen telling us that Jupiter doesn't want heretics thrown to the lions anymore, I agree that the epistemically rational thing to do is point out that we don't have much evidence for the efficacy of augury or the existence of Zeus, but the instrumentally rational thing to do is to smile, nod, and point out that eagles are well-known to convey the most urgent of omens. In more poetic words: you don't shoot soldiers on your side.
The metaphor seems to be as correct as any mere metaphor can get. Is it such a stretch to call an argument a "soldier" for you when it's responsible for helping defend your life, liberty, or property?
You seem to have excluded a middle option, namely "I am in favor of heretics not being thrown to the lions, and no amount of bird-related omen interpretation will sway my opinion on the subject one way or another."
Summary: I propose we somewhat relax our stance on political speech on Less Wrong.
Related: The mind-killer, Mind-killer
A recent series of posts by a well-meaning troll (example) has caused me to re-examine our "no-politics" norm. I believe there has been some unintentional creep from the original intent of Politics is the Mind-Killer. In that article, Eliezer is arguing that discussions here (actually on Overcoming Bias) should not use examples from politics in discussions that are not about politics, since they distract from the lesson. Note the final paragraph:
So, the original intent was not to ban political speech altogether, but to encourage us to come up with less-charged examples where possible. If the subject you're really talking about is politics, and it relates directly to rationality, then you should be able to post about it without getting downvotes strictly because "politics is the mind-killer".
It could be that this drift is less of a community norm than I perceive, and there are just a few folks (myself included) that have taken the original message too far. If so, consider this a message just to those folks such as myself.
Of course, politics would still be off-topic in the comment threads of most posts. There should probably be a special open thread (or another forum) to which drive-by political activists can be directed, instead of simply saying "We don't talk about politics here".
David_Gerard makes a similar point here (though FWIW, I came up with this title independently).